Ideal Theory

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Cambridge University Press, Jun 3, 2004 - Mathematics - 120 pages
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Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra. After a discussion of elementary ring theory, he deals with the properties of Noetherian rings and the algebraic and analytical theories of local rings. In order to give some idea of deeper applications of this theory the author has woven into the connected algebraic theory those results which play outstanding roles in the geometric applications.
 

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Contents

RESIDUE RINGS AND RINGS OF QUOTIENTS
31
the algebraic theory
63
Continuation of 4 3
81
Notes
101
References
110
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